MATE is not a "Gnome 2 fallback mode for Gnome 3". It's a complete fork of the old Gnome 2 codebase. In effect, it's Gnome 2. Nothing to do with Gnome 3 whatsoever. Cinnamon is a shell for Gnome 3. It sits on Gnome 3 like Gnome Shell and Unity, except Unity uses Compiz as a window manager instead of Mutter/Muffin.
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